\[ {}y^{\prime } = \frac {y \left (-1-x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2}-x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} \ln \left (x \right )+x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} y+2 x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} y \ln \left (x \right )+x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} x^{2} y \ln \left (x \right )^{2}\right )}{\left (\ln \left (x \right )+1\right ) x} \]

\[ {}y^{\prime } = \frac {y \left (-1-x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}}-x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} \ln \left (x \right )+x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} y+2 x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} y \ln \left (x \right )+x^{3} x^{\frac {2}{\ln \left (x \right )+1}} {\mathrm e}^{\frac {2 \ln \left (x \right )^{2}}{\ln \left (x \right )+1}} y \ln \left (x \right )^{2}\right )}{\left (\ln \left (x \right )+1\right ) x} \]

\[ {}y^{\prime } = \frac {2 x +4 y \ln \left (2 x +1\right ) x +6 y^{2} \ln \left (2 x +1\right ) x +6 y \ln \left (2 x +1\right )^{2} x +2 \ln \left (2 x +1\right )^{3} x +2 x y^{3}+2 \ln \left (2 x +1\right )^{2} x +2 x y^{2}-1+3 y^{2} \ln \left (2 x +1\right )+3 y \ln \left (2 x +1\right )^{2}+y^{2}+y^{3}+2 y \ln \left (2 x +1\right )+\ln \left (2 x +1\right )^{2}+\ln \left (2 x +1\right )^{3}}{2 x +1} \]

\[ {}y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \]

\[ {}y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{2} \sin \left (\frac {y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \]

\[ {}y^{\prime } = \frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2+2 y^{4}-4 y^{2} x^{2}+2 x^{4}+2 y^{6}-6 x^{2} y^{4}+6 x^{4} y^{2}-2 x^{6}}} \]

\[ {}y^{\prime } = \frac {4 x \left (a -1\right ) \left (1+a \right ) \left (-y^{2}+x^{2} a^{2}-x^{2}-2\right )}{-4 y^{3}+4 a^{2} x^{2} y-4 x^{2} y-8 y-a^{2} y^{6}+3 a^{4} y^{4} x^{2}-6 y^{4} a^{2} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}-4 a^{2} x^{6}+y^{6}+3 x^{2} y^{4}+3 x^{4} y^{2}+x^{6}} \]

\[ {}y^{\prime } = \frac {-4 x \cos \left (x \right )+4 x^{2} \sin \left (x \right )+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 x y+2 x^{2} \cos \left (2 x \right )+6 x^{2}-8 \cos \left (x \right ) x^{2}+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 x y^{2}+6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+x^{3} \cos \left (3 x \right )+15 x^{3} \cos \left (x \right )-6 x^{3} \cos \left (2 x \right )-10 x^{3}}{4 x} \]

\[ {}y^{\prime } = -\frac {8 x \left (a -1\right ) \left (1+a \right )}{8-8 y-2 y^{4} a^{2}+x^{6}-4 a^{2} x^{6}+2 x^{4}-8 a^{2}-6 y^{4} a^{2} x^{2}+y^{6}-a^{2} y^{6}+a^{8} x^{6}-4 a^{6} x^{6}+6 a^{4} x^{6}+3 x^{4} y^{2}+3 x^{2} y^{4}+4 y^{2} x^{2}+4 a^{4} y^{2} x^{2}+2 y^{4}-2 a^{6} x^{4}+6 a^{4} x^{4}-6 a^{2} x^{4}-8 y^{2} a^{2} x^{2}+3 a^{4} y^{4} x^{2}-3 a^{6} y^{2} x^{4}+9 y^{2} a^{4} x^{4}-9 y^{2} a^{2} x^{4}} \]

\[ {}y^{\prime } = \frac {-y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +2 \sin \left (\frac {y}{x}\right ) x^{3} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x} \]

\[ {}y^{\prime } = -\frac {1296 y}{216-1296 y-1728 y^{3}+216 x^{2}+216 x^{3}-2376 y^{2}-432 x y-882 y^{6}+216 x y^{2}-216 x^{2} y^{4}-846 y^{7}+1080 x y^{3}-648 y^{2} x^{2}-324 x^{2} y^{3}+1152 y^{4} x -570 y^{8}-315 y^{9}-126 y^{10}-8 y^{12}-36 y^{11}-648 x^{2} y-1944 y^{4}-612 y^{5}+1080 y^{5} x +594 x y^{6}+72 y^{8} x +216 y^{7} x} \]

\[ {}y^{\prime } = -\frac {x \left (-513-432 x -378 y-456 x^{6}+64 x^{9}-96 x^{8}-864 x^{4}-144 x^{7}-648 y^{3} x^{4}+432 y^{2} x^{7}+432 x^{3} y^{2}-216 y^{3}-216 y x^{4}-288 y x^{6}-1134 x^{2}-756 x^{3}-576 x^{5}-540 y^{2}+1008 x^{5} y-972 x^{4} y^{2}+720 x^{3} y-1296 y^{2} x^{2}-648 x^{2} y^{3}-594 x^{2} y-216 x^{6} y^{3}+864 y^{2} x^{5}-288 y x^{8}+288 y x^{7}-216 x^{6} y^{2}\right )}{216 \left (x^{2}+1\right )^{4}} \]

\[ {}y^{\prime } = \frac {-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )+2 \sin \left (\frac {y}{x}\right ) x^{4} \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )}{2 \cos \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x \left (1+x \right )} \]

\[ {}y^{\prime } = \frac {y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right ) x +y \sin \left (\frac {3 y}{2 x}\right ) \cos \left (\frac {y}{2 x}\right )+y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x +y \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right )-\sin \left (\frac {y}{x}\right ) y x -y \sin \left (\frac {y}{x}\right )+2 \sin \left (\frac {y}{x}\right ) \cos \left (\frac {y}{2 x}\right ) \sin \left (\frac {y}{2 x}\right ) x}{2 \cos \left (\frac {y}{x}\right ) \sin \left (\frac {y}{2 x}\right ) x \cos \left (\frac {y}{2 x}\right ) \left (1+x \right )} \]

\[ {}y^{\prime } = -\frac {216 y \left (-2 y^{4}-3 y^{3}-6 y^{2}-6 y+6 x +6\right )}{-1296 y+1728 y^{3}+216 x^{3}-1296 y^{2}-1296 x y+2484 y^{6}-1944 x y^{2}-216 x^{2} y^{4}+594 y^{7}-648 x y^{3}-648 y^{2} x^{2}-324 x^{2} y^{3}-432 y^{4} x -18 y^{8}-315 y^{9}-126 y^{10}-8 y^{12}-36 y^{11}-648 x^{2} y+2808 y^{4}+4428 y^{5}+1080 y^{5} x +594 x y^{6}+72 y^{8} x +216 y^{7} x} \]

\[ {}y^{\prime } = \frac {\left (x y+1\right )^{3}}{x^{5}} \]

\[ {}y^{\prime } = \frac {x \left (-x^{2}+2 x^{2} y-2 x^{4}+1\right )}{y-x^{2}} \]

\[ {}y^{\prime } = y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x} \]

\[ {}y^{\prime } = y^{3}-3 y^{2} x^{2}+3 y x^{4}-x^{6}+2 x \]

\[ {}y^{\prime } = y^{3}+y^{2} x^{2}+\frac {y x^{4}}{3}+\frac {x^{6}}{27}-\frac {2 x}{3} \]

\[ {}y^{\prime } = \frac {y \left (y^{2} x^{7}+y x^{4}+x -3\right )}{x} \]

\[ {}y^{\prime } = y \left (y^{2}+{\mathrm e}^{-x^{2}} y+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x \]

\[ {}y^{\prime } = \frac {y \left (y^{2}+x y+x^{2}+x \right )}{x^{2}} \]

\[ {}y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x} \]

\[ {}y^{\prime } = \frac {y^{3} x^{3}+6 y^{2} x^{2}+12 x y+8+2 x}{x^{3}} \]

\[ {}y^{\prime } = \frac {y^{3} a^{3} x^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+x \,a^{2}}{x^{3} a^{3}} \]

\[ {}y^{\prime } = \frac {y \,{\mathrm e}^{-\frac {x^{2}}{2}} \left (2 y^{2}+2 y \,{\mathrm e}^{\frac {x^{2}}{4}}+2 \,{\mathrm e}^{\frac {x^{2}}{2}}+x \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{2} \]

\[ {}y^{\prime } = \frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x^{2}}{\left (-1+x \right ) \left (1+x \right )} \]

\[ {}y^{\prime } = \frac {y \left (y^{2} x^{2}+y x \,{\mathrm e}^{x}+{\mathrm e}^{2 x}\right ) {\mathrm e}^{-2 x} \left (-1+x \right )}{x} \]

\[ {}y^{\prime } = \frac {\left (x y+1\right ) \left (y^{2} x^{2}+x^{2} y+2 x y+1+x +x^{2}\right )}{x^{5}} \]

\[ {}y^{\prime } = \frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 x^{2} \ln \left (x \right )^{2} y-x^{3} \ln \left (x \right )^{3}+x^{2}+x y}{x^{2}} \]

\[ {}y^{\prime } = -F \left (x \right ) \left (-x^{2} a +y^{2}\right )+\frac {y}{x} \]

\[ {}y^{\prime } = -F \left (x \right ) \left (-x^{2}-2 x y+y^{2}\right )+\frac {y}{x} \]

\[ {}y^{\prime } = -F \left (x \right ) \left (-a y^{2}-b \,x^{2}\right )+\frac {y}{x} \]

\[ {}y^{\prime } = -F \left (x \right ) \left (-y^{2}+2 x^{2} y+1-x^{4}\right )+2 x \]

\[ {}y^{\prime } = -F \left (x \right ) \left (x^{2}+2 x y-y^{2}\right )+\frac {y}{x} \]

\[ {}y^{\prime } = -F \left (x \right ) \left (-7 x y^{2}-x^{3}\right )+\frac {y}{x} \]

\[ {}y^{\prime } = -F \left (x \right ) \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{\ln \left (x \right ) x} \]

\[ {}y^{\prime } = -x^{3} \left (-y^{2}-2 y \ln \left (x \right )-\ln \left (x \right )^{2}\right )+\frac {y}{\ln \left (x \right ) x} \]

\[ {}y^{\prime } = \left (y-{\mathrm e}^{x}\right )^{2}+{\mathrm e}^{x} \]

\[ {}y^{\prime } = \frac {\left (y-\operatorname {Si}\left (x \right )\right )^{2}+\sin \left (x \right )}{x} \]

\[ {}y^{\prime } = \left (y+\cos \left (x \right )\right )^{2}+\sin \left (x \right ) \]

\[ {}y^{\prime } = \frac {\left (y-\ln \left (x \right )-\operatorname {Ci}\left (x \right )\right )^{2}+\cos \left (x \right )}{x} \]

\[ {}y^{\prime } = \frac {\left (y-x +\ln \left (1+x \right )\right )^{2}+x}{1+x} \]

\[ {}y^{\prime } = \frac {2 x^{2} y+x^{3}+y \ln \left (x \right ) x -y^{2}-x y}{x^{2} \left (x +\ln \left (x \right )\right )} \]

\[ {}y^{\prime } = f \left (x \right ) \]

\[ {}y^{\prime } = f \left (y\right ) \]

\[ {}y^{\prime } = f \left (x \right ) g \left (y\right ) \]

\[ {}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{0} \left (x \right ) \]

\[ {}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n} \]

\[ {}y^{\prime } = f \left (\frac {y}{x}\right ) \]

\[ {}y^{\prime } = a y^{2}+b x +c \]

\[ {}y^{\prime } = y^{2}-x^{2} a^{2}+3 a \]

\[ {}y^{\prime } = y^{2}+x^{2} a^{2}+b x +c \]

\[ {}y^{\prime } = a y^{2}+b \,x^{n} \]

\[ {}y^{\prime } = y^{2}+a n \,x^{n -1}-a^{2} x^{2 n} \]

\[ {}y^{\prime } = a y^{2}+b \,x^{2 n}+c \,x^{n -1} \]

\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{-n -2} \]

\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} \]

\[ {}y^{\prime } = y^{2}+k \left (a x +b \right )^{n} \left (c x +d \right )^{-n -4} \]

\[ {}y^{\prime } = a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m} \]

\[ {}y^{\prime } = \left (a \,x^{2 n}+b \,x^{n -1}\right ) y^{2}+c \]

\[ {}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0} = 0 \]

\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \]

\[ {}x^{2} y^{\prime } = y^{2} x^{2}-a^{2} x^{4}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right ) \]

\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \,x^{n}+c \]

\[ {}x^{2} y^{\prime } = y^{2} x^{2}+a \,x^{2 m} \left (b \,x^{m}+c \right )^{n}-\frac {n^{2}}{4}+\frac {1}{4} \]

\[ {}\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} = 0 \]

\[ {}x^{4} y^{\prime } = -x^{4} y^{2}-a^{2} \]

\[ {}a \,x^{2} \left (-1+x \right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s = 0 \]

\[ {}\left (x^{2} a +b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \]

\[ {}x^{n +1} y^{\prime } = a \,x^{2 n} y^{2}+c \,x^{m}+d \]

\[ {}\left (a \,x^{n}+b \right ) y^{\prime } = b y^{2}+a \,x^{n -2} \]

\[ {}\left (a \,x^{n}+b \,x^{m}+c \right ) \left (y^{\prime }-y^{2}\right )+a n \left (n -1\right ) x^{n -2}+b m \left (m -1\right ) x^{m -2} = 0 \]

\[ {}y^{\prime } = a y^{2}+b y+c x +k \]

\[ {}y^{\prime } = y^{2}+a \,x^{n} y+a \,x^{n -1} \]

\[ {}y^{\prime } = y^{2}+a \,x^{n} y+b \,x^{n -1} \]

\[ {}y^{\prime } = y^{2}+\left (\alpha x +\beta \right ) y+x^{2} a +b x +c \]

\[ {}y^{\prime } = y^{2}+a \,x^{n} y-a b \,x^{n}-b^{2} \]

\[ {}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +m +1}-a \,x^{m} \]

\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+b c \,x^{m}-a \,c^{2} x^{n} \]

\[ {}y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,x^{m}+c \right ) y+b m \,x^{m -1} \]

\[ {}y^{\prime } = -a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m} \]

\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+c k \,x^{k -1}-b c \,x^{m +k}-a \,c^{2} x^{n +2 k} \]

\[ {}x y^{\prime } = a y^{2}+b y+c \,x^{2 b} \]

\[ {}x y^{\prime } = a y^{2}+b y+c \,x^{n} \]

\[ {}x y^{\prime } = a y^{2}+\left (n +b \,x^{n}\right ) y+c \,x^{2 n} \]

\[ {}x y^{\prime } = x y^{2}+a y+b \,x^{n} \]

\[ {}x y^{\prime }+a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0} = 0 \]

\[ {}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{-n} \]

\[ {}x y^{\prime } = a \,x^{n} y^{2}+m y-a \,b^{2} x^{n +2 m} \]

\[ {}x y^{\prime } = x^{2 n} y^{2}+\left (m -n \right ) y+x^{2 m} \]

\[ {}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{m} \]

\[ {}x y^{\prime } = a \,x^{2 n} y^{2}+\left (b \,x^{n}-n \right ) y+c \]

\[ {}x y^{\prime } = a \,x^{2 n +m} y^{2}+\left (b \,x^{m +n}-n \right ) y+c \,x^{m} \]

\[ {}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (a_{1} x +b_{1} \right ) y+a_{0} x +b_{0} = 0 \]

\[ {}\left (a x +c \right ) y^{\prime } = \alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma \]

\[ {}2 x^{2} y^{\prime } = 2 y^{2}+x y-2 x \,a^{2} \]

\[ {}2 x^{2} y^{\prime } = 2 y^{2}+3 x y-2 x \,a^{2} \]

\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \]